## College Algebra (11th Edition)

$\dfrac{\sqrt{15p}}{3p}$
$\bf{\text{Solution Outline:}}$ Use the laws of radicals to simplify the given expression, $\sqrt{\dfrac{5}{3p}} .$ Then rationalize the denominator. $\bf{\text{Solution Details:}}$ Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{5}}{\sqrt{3p}} .\end{array} Rationalizing the denominator results to \begin{array}{l}\require{cancel} \dfrac{\sqrt{5}}{\sqrt{3p}}\cdot\dfrac{\sqrt{3p}}{\sqrt{3p}} \\\\= \dfrac{\sqrt{5(3p)}}{(\sqrt{3p})^2} \text{ (product rule)} \\\\= \dfrac{\sqrt{15p}}{3p} .\end{array}